Using beam-stacked data to check the estimation results

When a velocity model to be used for depth migration is built, it is important to use the prestack data to check the quality of the results. The beam-stacked data can be readily used for this purpose of quality check: the actual position of the semblance peaks in the beam-stacked data can be compared with the positions predicted by the estimated velocity model.

I sliced the beam stacks at the traveltimes corresponding to the reflector at about 4.5 km in the migrated section of Figure . Figure  shows semblance, as a function of the transformed offset and midpoint location, and for a fixed p_h equal to 0.076 s/km and p_y equal to zero. The thinner line superimposed to the semblance plot corresponds to the transformed offsets predicted by the background velocity, and the thicker line corresponds to the transformed offsets predicted by the estimated velocity. The peaks of the beam stacks are well predicted by the final results of the estimation.

One of the main advantages of estimating velocity with local stacking operators, such as beam stacks, is the possibility of inverting data that depend locally on the moveouts of the reflections. This advantage would be only theoretical if the resolution of beam stacks were not sufficient to obtain independent measures for different offset ray parameters. Figure  shows that it is actually possible to measure the different effects of the velocity anomaly on the reflections having different offset ray parameters. The three panels show slices of the beam-stacked data taken at three midpoint locations, and for the same reflector as in Figure , but as a function of p_h. In this figure the thinner line superimposed to the semblance plot corresponds to the transformed offsets predicted by the background velocity, and the thicker line corresponds to the transformed offsets predicted by the estimated velocity. The first and the third panel correspond to midpoints located on the side of the anomaly, and consequently the reflections with higher p_h were more strongly affected by the anomaly than were the ones with lower p_h. On the contrary the panel on the center corresponds to a midpoint located at the center of the anomaly, and consequently the reflections with lower p_h were more strongly affected by the anomaly than were the ones with higher p_h. It is useful to notice that the beam stacks are zero for p_h higher than 0.206 s/km because the corresponding reflections would have been recorded off the end of the cable.